x/2-2=2x^2+x-3

Solution for x/2-2=2x^2+x-3 equation:

x/2-2=2x^2+x-3

We move all terms to the left:

x/2-2-(2x^2+x-3)=0

We get rid of parentheses

-2x^2+x/2-x+3-2=0

We multiply all the terms by the denominator


-2x^2*2+x-x*2+3*2-2*2=0

We add all the numbers together, and all the variables

-2x^2*2+x-x*2+2=0

Wy multiply elements

-4x^2+x-2x+2=0

We add all the numbers together, and all the variables

-4x^2-1x+2=0

a = -4; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-4)·2
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{33}}{2*-4}=\frac{1-\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*-4}=\frac{1+\sqrt{33}}{-8}
$